Christian Lubich's Books

Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

By: Ernst Hairer,Christian Lubich,Gerhard Wanner

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Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

By: Ernst Hairer,Christian Lubich,Gerhard Wanner

This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.

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526

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662050188

ISBN 13

9783662050187

The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods

By: Ernst Hairer,Christian Lubich,Michel Roche

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The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods

By: Ernst Hairer,Christian Lubich,Michel Roche

The term differential-algebraic equation was coined to comprise differential equations with constraints (differential equations on manifolds) and singular implicit differential equations. Such problems arise in a variety of applications, e.g. constrained mechanical systems, fluid dynamics, chemical reaction kinetics, simulation of electrical networks, and control engineering. From a more theoretical viewpoint, the study of differential-algebraic problems gives insight into the behaviour of numerical methods for stiff ordinary differential equations. These lecture notes provide a self-contained and comprehensive treatment of the numerical solution of differential-algebraic systems using Runge-Kutta methods, and also extrapolation methods. Readers are expected to have a background in the numerical treatment of ordinary differential equations. The subject is treated in its various aspects ranging from the theory through the analysis to implementation and applications.

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Page Count

146

Publisher

Springer

Published Date

ISBN 10

3540468323

ISBN 13

9783540468325

From Quantum to Classical Molecular Dynamics

Reduced Models and Numerical Analysis

By: Christian Lubich

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From Quantum to Classical Molecular Dynamics

Reduced Models and Numerical Analysis

By: Christian Lubich

Quantum dynamics of molecules poses a variety of computational challenges that are presently at the forefront of research efforts in numerical analysis in a number of application areas: high-dimensional partial differential equations, multiple scales, highly oscillatory solutions, and geometric structures such as symplecticity and reversibility that are favourably preserved in discretizations. This text addresses such problems in quantum mechanics from the viewpoint of numerical analysis, illustrating them to a large extent on intermediate models between the Schrodinger equation of full many-body quantum dynamics and the Newtonian equations of classical molecular dynamics. The fruitful interplay between quantum dynamics and numerical analysis is emphasized.

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Page Count

164

Publisher

European Mathematical Society

Published Date

ISBN 10

3037190671

ISBN 13

9783037190678

Geometric Theory of Discrete Nonautonomous Dynamical Systems

By: Christian Pötzsche

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Geometric Theory of Discrete Nonautonomous Dynamical Systems

By: Christian Pötzsche

Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.

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Page Count

422

Publisher

Springer

Published Date

ISBN 10

3642142583

ISBN 13

9783642142581

Numerics of Unilateral Contacts and Friction

Modeling and Numerical Time Integration in Non-Smooth Dynamics

By: Christian Studer

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Numerics of Unilateral Contacts and Friction

Modeling and Numerical Time Integration in Non-Smooth Dynamics

By: Christian Studer

Mechanics provides the link between mathematics and practical engineering app- cations. It is one of the oldest sciences, and many famous scientists have left and will leave their mark in this fascinating ?eld of research. Perhaps one of the most prominentscientists in mechanics was Sir Isaac Newton, who with his “laws of - tion” initiated the description of mechanical systems by differential equations. And still today, more than 300 years after Newton, this mathematical concept is more actual than ever. The rising computer power and the development of numerical solvers for diff- ential equations allowed engineersall over the world to predict the behavior of their physical systems fast and easy in an numerical way. And the trend to computational simulation methods is still further increasing, not only in mechanics, but practically in all branches of science. Numerical simulation will probablynot solve the world’s engineering problems, but it will help for a better understanding of the mechanisms of our models.

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Page Count

182

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642011004

ISBN 13

9783642011009

15 Days of Prayer with Blessed Frédéric Ozanam

By: Christian Verheyde

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15 Days of Prayer with Blessed Frédéric Ozanam

By: Christian Verheyde

15 Days of Prayer with Blessed Frederic marks the 200th anniversary of Ozanam's birth. Verheyde's meditations reflect the breadth of Ozanam's interests: his love for his family; his desire to proclaim the faith authentically.

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Page Count

139

Publisher

New City Press

Published Date

ISBN 10

1565484878

ISBN 13

9781565484870

Multiple Time Scale Dynamics

By: Christian Kuehn

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Multiple Time Scale Dynamics

By: Christian Kuehn

This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.

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Page Count

816

Publisher

Springer

Published Date

ISBN 10

3319123165

ISBN 13

9783319123165

Wave Phenomena

Mathematical Analysis and Numerical Approximation

By: Willy Dörfler,Marlis Hochbruck,Jonas Köhler,Andreas Rieder,Roland Schnaubelt,Christian Wieners

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Wave Phenomena

Mathematical Analysis and Numerical Approximation

By: Willy Dörfler,Marlis Hochbruck,Jonas Köhler,Andreas Rieder,Roland Schnaubelt,Christian Wieners

This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach. The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing. The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.

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Page Count

368

Publisher

Springer Nature

Published Date

ISBN 10

3031057937

ISBN 13

9783031057939

Uncertainty Quantification

An Accelerated Course with Advanced Applications in Computational Engineering

By: Christian Soize

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Uncertainty Quantification

An Accelerated Course with Advanced Applications in Computational Engineering

By: Christian Soize

This book presents the fundamental notions and advanced mathematical tools in the stochastic modeling of uncertainties and their quantification for large-scale computational models in sciences and engineering. In particular, it focuses in parametric uncertainties, and non-parametric uncertainties with applications from the structural dynamics and vibroacoustics of complex mechanical systems, from micromechanics and multiscale mechanics of heterogeneous materials. Resulting from a course developed by the author, the book begins with a description of the fundamental mathematical tools of probability and statistics that are directly useful for uncertainty quantification. It proceeds with a well carried out description of some basic and advanced methods for constructing stochastic models of uncertainties, paying particular attention to the problem of calibrating and identifying a stochastic model of uncertainty when experimental data is available. This book is intended to be a graduate-level textbook for students as well as professionals interested in the theory, computation, and applications of risk and prediction in science and engineering fields.

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Page Count

344

Publisher

Springer

Published Date

ISBN 10

3319543393

ISBN 13

9783319543390

The Boundary Element Method with Programming

For Engineers and Scientists

By: Gernot Beer,Ian Smith,Christian Duenser

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The Boundary Element Method with Programming

For Engineers and Scientists

By: Gernot Beer,Ian Smith,Christian Duenser

This thorough yet understandable introduction to the boundary element method presents an attractive alternative to the finite element method. It not only explains the theory but also presents the implementation of the theory into computer code, the code in FORTRAN 95 can be freely downloaded. The book also addresses the issue of efficiently using parallel processing hardware in order to considerably speed up the computations for large systems. The applications range from problems of heat and fluid flow to static and dynamic elasto-plastic problems in continuum mechanics.

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Page Count

496

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3211715762

ISBN 13

9783211715765

Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

By: Ernst Hairer,Christian Lubich,Gerhard Wanner

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Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

By: Ernst Hairer,Christian Lubich,Gerhard Wanner

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Write a review

Solve jigsaw puzzle

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Page Count

526

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3662050188

ISBN 13

9783662050187

Book's by Christian Lubich

Geometric Numerical Integration

Geometric Numerical Integration

The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods

The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods

From Quantum to Classical Molecular Dynamics

From Quantum to Classical Molecular Dynamics

Geometric Theory of Discrete Nonautonomous Dynamical Systems

Geometric Theory of Discrete Nonautonomous Dynamical Systems

Numerics of Unilateral Contacts and Friction

Numerics of Unilateral Contacts and Friction

15 Days of Prayer with Blessed Frédéric Ozanam

15 Days of Prayer with Blessed Frédéric Ozanam

Multiple Time Scale Dynamics

Multiple Time Scale Dynamics

Wave Phenomena

Wave Phenomena

Uncertainty Quantification

Uncertainty Quantification

The Boundary Element Method with Programming

The Boundary Element Method with Programming

Geometric Numerical Integration

Geometric Numerical Integration

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